1. Field of the Invention
The present invention relates to an information processing apparatus and method, a program and a recording medium, and more particularly to an information processing apparatus and method, a program and a recording medium, suitable for utilizing measurement results of radio wave incident angles of received signals.
2. Description of Related Art
Wireless communications conforming to the specifications of Institute of Electrical and Electronics Engineers (IEEE) 802.11n are prevailing.
In IEEE 802.11n, information is transmitted and received by using a non-directional antenna, and a physical layer of a receiver system can detect an incident angle of a radio wave when the radio wave is received. However, it is not easy to judge whether the radio wave received at the receiver system arrives directly from a transmitter side or a radio wave arrives after it is reflected by a wall or the like. For example, as shown in FIG. 1 a radio wave transmitted from a transmitter system 1 is received at a receiver system 2 at some incident angle. However, if portion of the radio wave is reflected by an obstacle 3 such as a wall and the portion arrives at a different angle, the radio wave received at the receiver system 2 has two or more incident angles.
In IEEE 802.11n, an orthogonal frequency division multiplexing (OFDM) modulation scheme is used as a scheme for realizing high speed data transfer by wireless communications. The OFDM modulation scheme is a multi carrier modulation scheme for transmitting a signal multiplexing digital modulation waves and having 10 to 100 to several thousand orthogonal carrier frequencies.
The OFDM technique allows, as described above, the physical layer of a receiver system to detect an incident angle of a radio wave when the radio wave is received. For example, the radio wave incident angle may be detected by obtaining a spatial spectrum.
In extracting a desired signal from a signal which is a mixture of the desired signal and an interference signal or in measuring an impulse response of a channel, it may become necessary to measure an incident direction of a signal. Accordingly, there is also an algorithm for more accurately measuring a signal incident direction. Algorithms for estimating a signal incident direction by using an array antenna include, for example, a Fourier transform method, a maximum entropy method, a method based upon eigenvalue expansion and the like. One of the methods based upon eigenvalue expansion is a method of detecting a radio wave incident angle by using a MUltiple SIgnal Classification (MUSIC) method (for example, refer to R. O. Schmit, “Multiple Emitter Location and Signal Parameter Estimation”, IEEE Trans., vol. AP-34, No. 3, pp. 276-280, March 1986).
Description will be made next on techniques for detecting a radio wave incident angle by obtaining a spatial spectrum and techniques for detecting a radio wave incident angle by using a MUSIC algorithm.
FIG. 2 shows the structure of an array antenna constituted of M+1 antenna elements.
Of M+1 antenna elements constituted of an antenna 0 to an antenna M, the position of the antenna 0 is used as a reference position, and the antennas 1 to M are located at distances d1, d2, . . . , dM.
In order to estimate a signal incident angle by using the array antenna, it is necessary to clarify the relationship between an antenna element position and an incident radio wave.
Now, it is assumed that a signal represented by the following formula (1) arrives at the antenna 0.v(t)=s(t)exp(jωct)  (1)
In the formula, v(t) is a complex band signal, s(t) is a complex baseband signal, and ωc=2πfc is an angular frequency of a carrier. The same signal as that represented by the formula (1) is received also at the antenna 1 with a path difference 11. Representing a signal incident direction by φ, the path difference 11 is given by the following formula (2).I1=−d1 sin(φ)  (2)
An incident time difference τ caused by the path difference is given by the following formula (3).τ=I1/c=2πI1/ωcλ  (3)
In this formula, c is the light velocity and λ is a carrier wavelength.
Accordingly, a received signal at the antenna 1 is given by the following formula (4).
                                                                        v                ⁡                                  (                  t                  )                                            =                            ⁢                                                s                  ⁡                                      (                                          t                      -                      τ                                        )                                                  ⁢                                  exp                  ⁡                                      (                                                                  jω                        c                                            ⁢                      t                                        )                                                  ⁢                                  exp                  ⁡                                      (                                                                  -                                                  jω                          c                                                                    ⁢                      t                                        )                                                                                                                          =                            ⁢                                                s                  ⁡                                      (                                          t                      -                      τ                                        )                                                  ⁢                                  exp                  ⁡                                      (                                                                  jω                        c                                            ⁢                      t                                        )                                                  ⁢                                  exp                  ⁡                                      (                                          j                      ⁢                                                                                          ⁢                      2                      ⁢                      π                      ⁢                                                                                          ⁢                                              d                        1                                            ⁢                                                                        sin                          ⁡                                                      (                            ϕ                            )                                                                          /                        λ                                                              )                                                                                                          (        4        )            
Typically, τ can be neglected because it is very short relative to the period of the signal s(t). Therefore, the formula (4) can be rewritten by the following formula (5)v(t)=s(t)exp(jωct)exp(j2πd1 sin(φ)/λ)  (5)A complex baseband signal of the first antenna after frequency conversion can be given by the following formula (6). Similarly, a complex baseband signal of the m-th antenna can be given by the following formula (7).r1(t)=s(t)exp(j2πd1 sin(φ)/λ)  (6)rm(t)=s(t)exp(j2λdm sin(φ)/λ)  (7)
Accordingly, if the received signal at each antenna is subject to discrete Fourier transform, the following formulas (8) and (9) can be obtained.
                                          R            1                    ⁡                      (            t            )                          =                              σ                          m              =              0                                      M              -              1                                ⁢                                    r              m                        ⁡                          (              t              )                                ⁢                      exp            ⁡                          (                              j                ⁢                                                                  ⁢                2                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                                  ml                  /                  M                                            )                                                          (        8        )                                                      R            1                    ⁡                      (            t            )                          =                              s            ⁡                          (              t              )                                ⁢                                    1              -                              exp                ⁢                                  (                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                                          M                      ⁡                                              (                                                                              d                            ⁢                                                                                                                  ⁢                            sin                            ⁢                                                                                                                  ⁢                                                          ϕ                              /                              λ                                                                                +                                                      1                            /                            M                                                                          )                                                                              )                                                                    1              -                              exp                ⁡                                  (                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                                          π                      ⁡                                              (                                                                              d                            ⁢                                                                                                                  ⁢                            sin                            ⁢                                                                                                                  ⁢                                                          ϕ                              /                              λ                                                                                +                                                      1                            /                            M                                                                          )                                                                              )                                                                                        (        9        )            
With the above calculation processing, a spatial spectrum of the received signals can be obtained, making it possible to obtain the incident angle φ of the received signal.
FIG. 3 shows an example of a spatial spectrum in which a signal arrives at an antenna array from the front side, i.e., at an incident angle φ=0 degree, the antenna array having eight antennas disposed at an equal interval of a half wavelength.
Description will be made next on estimation of an incident direction by MUSIC.
Consider now that uncorrelated signals of L waves arrive at the array antenna constituted of M+1 (L≦M) antenna, elements described with reference to FIG. 2. By representing an incident direction of each signal by φ1, a received signal rm(t) at the m-th antenna element is represented by the following formula (10).
                                          r            m                    ⁡                      (            t            )                          =                                            ∑                              l                =                1                            L                        ⁢                                                            P                  1                                            ⁢                                                s                  1                                ⁡                                  (                  t                  )                                            ⁢                              exp                ⁡                                  (                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                                          d                      m                                        ⁢                                                                  sin                        ⁡                                                  (                                                      ϕ                            1                                                    )                                                                    /                      λ                                                        )                                                              +                                    n              m                        ⁡                          (              t              )                                                          (        10        )            
In this formula, a root of P1 is a power of a first wave signal, s1(t) is a transmission signal of the 1st wave, dm is a distance from the 0-th antenna element to the m-th antenna element, φ1 is an incident angle of the l-th signal, λ is a wavelength, and nm is noise generated when the signal is received at the m-th antenna element.
A mutual correlation matrix R of received signals can be represented by the following formula (11) by representing a variance of noises by σ2. In the formula (11), the following formulas (12), (13) and (14) are satisfied.
                                                        R              =                            ⁢                                                SDS                  H                                +                                  σ                  2                                                                                                        S              =                            ⁢                              [                                                      s                    1                                    ,                                      s                    2                                    ,                  ⋯                  ⁢                                                                          ,                                      s                    L                                                  ]                                                                                                        =                                ⁢                                  [                                                                                    1                                                                    1                                                                    ⋯                                                                    1                                                                                                                                      exp                          ⁡                                                      (                                                          j                              ⁢                                                                                                                          ⁢                                                              ω                                11                                                                                      )                                                                                                                                                exp                          ⁡                                                      (                                                          j                              ⁢                                                                                                                          ⁢                                                              ω                                12                                                                                      )                                                                                                                      ⋯                                                                                              exp                          ⁡                                                      (                                                          jω                                                              1                                ⁢                                                                                                                                  ⁢                                L                                                                                      )                                                                                                                                                                                        exp                          ⁡                                                      (                                                          jω                              21                                                        )                                                                                                                                                exp                          ⁡                                                      (                                                          j                              ⁢                                                                                                                          ⁢                                                              ω                                22                                                                                      )                                                                                                                      ⋯                                                                                              exp                          ⁡                                                      (                                                          jω                                                              2                                ⁢                                                                                                                                  ⁢                                L                                                                                      )                                                                                                                                                              ⋮                                                                    ⋮                                                                    ⋱                                                                    ⋮                                                                                                                                      exp                          ⁡                                                      (                                                          jω                                                              M                                ⁢                                                                                                                                  ⁢                                1                                                                                      )                                                                                                                                                exp                          ⁡                                                      (                                                          jω                                                              M                                ⁢                                                                                                                                  ⁢                                2                                                                                      )                                                                                                                      ⋯                                                                                              exp                          ⁡                                                      (                                                          jω                              ML                                                        )                                                                                                                                ]                                            ,                                                                                          ω                                  m                  ⁢                                                                          ⁢                  1                                            =                            ⁢                              2                ⁢                π                ⁢                                                                  ⁢                                  d                  m                                ⁢                                                      sin                    ⁡                                          (                                              ϕ                        1                                            )                                                        /                  λ                                                                                                        D              =                            ⁢                              diag                ⁡                                  (                                                            P                      1                                        ,                                          P                      2                                        ,                    ⋯                    ⁢                                                                                  ,                                          P                      L                                                        )                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                (                                                        11                                                        )                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  (                                      12                                      )                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      (                    13                    )                                                                                                                          (              14              )                                          
In order to estimate an incident direction by using the MUSIC method, it is necessary to obtain eigenvalues and eigenvectors of the correlation matrix of input signals to the array antenna. The following formulas (15) stand by representing the eigenvalues of the correlation matrix R by λ0≧λ1≧ . . . ≧λM and by representing the eigenvalues of SDSH by v0≧v1≧ . . . ≧VM.
                              λ          i                =                  {                                                                                          ν                    i                                    +                                      σ                    2                                                                                                                    i                    =                    0                                    ,                  ⋯                  ⁢                                                                          ,                                      L                    -                    1                                                                                                                        σ                  2                                                                                                  i                    =                    L                                    ,                  ⋯                  ⁢                                                                          ,                  M                                                                                        (        15        )            
Namely, it is possible to assume that the number of eigenvalues larger than the variance σ2 of noises is the number of incident signals arriving at the array antenna.
For example, if the eigenvalues of the correlation matrix of received signals are in the state as shown in FIG. 4, the number of eigenvalues larger than the variance σ2 of noises is four. It is therefore possible to estimate that the number of incident signals is four.
By representing the eigenvectors corresponding to the eigenvalues λ0, λ1, . . . , λM by q0, q1, . . . , qM, a relationship shown in the following formula (16) can be derived.sIHqi=0, I=1,2, . . . i=L, . . . , M.  (16)
A MUSIC spectrum is defined by the following formula (17).
                                          P            MU                    ⁡                      (            ϕ            )                          =                                                            s                H                            ⁡                              (                ϕ                )                                      ⁢                          s              ⁡                              (                ϕ                )                                                                        ∑                              i                =                L                            M                        ⁢                                                                                                q                    i                    H                                    ⁢                                      s                    ⁡                                          (                      ϕ                      )                                                                                                  2                                                          (        17        )            
The MUSIC spectrum has L peaks because of the relationship indicated by the formula (16). A value φ corresponding to each peak is a signal incident angle.
FIG. 5 shows simulation results adopting the MUSIC algorithm for signals having incident angles of 10° and 30° received at a three-element array antenna. This simulation does not consider noises.